Marine Current Turbine System Post-Fault Behavior under an Open Circuit Fault

This paper describes the modeling and simulation of a Permanent Magnet Synchronous Generator (PMSG) based Marine Current Turbine (MCT) under converter faulty conditions. The modeling of the generator is represented in the d-q reference frame. The Proportional Integral (PI) controllers are used for the direct current, the quadratic current, and the speed Control. The faulty mode describes an open-circuit fault in the generator-side converter. Simulations results show that the dynamic performances and the power generation of the MCT are highly degraded due to the fault.


Introduction
Nowadays, new renewable resources are developed such as wave energy, thermal energy, and marine tidal energy.In fact, the production of electric power from marine tidal energy is interesting; 48 % is in the UK, 8 % in Ireland, and 42 % in France [1].
However, marine current turbine systems are exposed to ecological constraints because of the severe weather conditions (immersed systems).Due to these constraints, the performance of the MCT system can be degraded [2] and [3].That leads to several faults, which can be related to the PMSG, to the blades, and to the converters [4] and [5].Indeed, industrial surveys have shown that 70 % of converter faults are related to the switches.
This paper describes the modeling of the MCT system under switchs fault conditions (open circuit fault).The control of the MCT system is achieved by using the Maximum Power Point Tracking (MPPT) to extract the optimal power and the PI controllers are designed to control the dq-axis currents and the speed.
This paper is composed as follows: in Sec. 2. , the MCT system modeling is given.In Sec. 3. , MCT system control is developed.In Sec. 4. , post-fault behavior of the generator-side converter and performance evaluation are analyzed.Section 5. gives the conclusion.

Marine Current Turbine Modeling
Figure 1 represents the MCT basic structure.It contains the turbine, the PMSG, the three-phase converter and the DC-bus.
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Resource Description
The gravitational interaction of Moon, Earth, and Sun creates the marine currents [6].Marine currents are resulted about 32 % from the Sun and 68 % from the Moon.In fact, this interaction makes the ocean swell on different places.This fact makes an increase of the altitude of the water in the aligned places with the moon and a decrease in the level of the water between those two places.A horizontal movement is resulted from the increase in water level; this movement is called tidal current.

Marine Turbine Model
A marine turbine mechanical power is given by Eq. (1) [7].
where ρ is the fluid density in (kg•m −3 ), r is the turbine radius in (m), v t is the tidal velocity in (m•s −1 ), C p represents the rate of mechanical power extracted by the turbine from the fluid, λ is the tip speed ratio, and β is the blade pitch angle in ( • ).For typical MCTs and under normal operation, the maximum value of C p is in the range of 0.35-0.5.In fact, for a given turbine, the power coefficient is represented using λ (Eq.( 2)) and β [8].
where Ω is the mechanical turbine speed in (rpm).

Generator Model
The PMSG was chosen for the system [9] thanks to its high efficiency, its compactness, and the possibility to remove gearbox in case of a direct-drive system.This reduces maintenance and makes the PMSG as a candidate of choice for immersed systems.The modeling of PMSG in the d-q reference is given by Eq. ( 3) as follows: where , v sd and v sq are the d − q components of the stator voltages respectively in (V), i sd and i sq are the d − q components of the stator currents respectively in (A), R s is the phase resistance of the stator winding in (Ω), L s is the stator cyclic inductance in (H), Φ a is the permanent magnet flux in (Wb) and p is the pole pair number.

Converter Model
The generator-side converter contains three legs (Fig. 2).Every leg is composed by two switches (T k ,

Marine Current Turbine Control
The marine current turbine control system is based on a PI controller, which is used in conventional fieldoriented control technique.It is illustrated by Fig. 3.

Maximum Power Point Tracking
The control system is defined by Eq. ( 5) as follows: where (ω = pΩ) is the electrical speed, ψ sd and ψ sq are the d − q components of the stator flux, respectively, defined by Eq. ( 6) as follows: The MPPT strategy is based on a variable speed [11].Indeed, the rotor speed is controlled using a PI controller to obtain the value of λ that corresponds to the maximum value of the power coefficient C p and finally achieve the expected maximum power by the MCT.
The speed controller is given by Eq. ( 7) as follows: where b 1 is the controller proportional coefficient and b 0 is the controller integral.
The placing poles technique is used to compute the parameters of this controller.The reference of the speed is expressed by Eq. (8).It is used in order to make the function of the turbine is around the maximum power for different current tidal velocities.
If the tidal velocity exceeds 2.3 m•s −1 [12], the power is restricted to 7.5 kW.The power of the turbine for different tidal velocities is determined by Eq. (1).

Current PI Controller
The PI currents controllers are given by Eq. ( 9) as follows: where k p is the controller proportional coefficient and k i is the controller integral.The division compensation technique is used to complete the parameters of these controllers.To reduce resistive losses, the reference of the d-axis current is zero, so, the q-axis current is the only current which control the electromagnetic torque.
The reference of the quadratic current is determined via the controller of the speed.The converter voltage vector is given by the two PI currents controllers.The control signal is generated by the PWM block to implement the vector control of the generator.

Marine Current Turbine Post-Fault Behavior and Results Analysis
In this section, the influence of an open-circuit fault on the PMSG phase currents and the MCT dynamic performances will be studied on a PMSG-based MCT whose parameters are given in the Appendix.Simulations are carried out using MATLAB/Simulink environment.Figure 4   Waveforms given by Fig. 5 and Fig. 6 shows the three phase currents, the line-to-line voltage U AB , and the load voltage V AN , respectively.In Fig. 6, a fault state is introduced at t = 1.02 s and applied to the switch (T1).It is observed that the phase cur-rent ia is no more negative (Fig. 5(a)).The lineto-line voltage U AB (Fig. 5(c)) and the load voltage V AN (Fig. 5(e)) exhibit a great drop from the positive level to the negative one.at t = 1.0295 s, taking 9.5 ms as fault detection time.In Fig. 6, the fault is now applied to the switch (T4), the reverse effect is observed on the phase current ia (Fig. 6   figures, by using PI control, the power, the speed, and the torque have some ripples at the faults occurrence. Figure 10 gives a histogram which shows the range of variation in speed, torque, and power in (%) at t = 1 s.This proves that this technique is not useful and does not present any robustness against faults, therefore leading to the MCT system performances degradation.

Conclusion
The paper described the simulation of a PMSG-based marine current turbine experiencing open-circuit fault in power switches of its generator-side converter.PI controllers have been adopted for the MCT control.These results evidently show that PI control is very sensitive to faulty conditions and does not present any robustness.Therefore a fault-tolerant rectifier with specific redundancy or an advanced robust control techniques such as a high order sliding mode control are required.
represents an example of marine current velocity in the Raz de Sein (potential site for the MCT project of the coast of Brittany in France) during 20 s based on tidal current data given by the French Navy Hydrographic and Oceanographic Service (SHOM).The marine current velocity can reach 2.3 m•s −1 .Load voltage.
(a)), the line-to-line voltage U AB (Fig.6(b)), and the load voltage V AN (Fig.6(c)) exhibit a great drop from the negative level to the positive one.

Figure 7 ,
Fig.8, and Fig.9represent the generated power, the rotor speed, and the torque with its version.It should be noticed that these results are achieved for an open-circuit in switch T1 occurring at t = 1 s, t = 4 s, t = 8 s and t = 17 s.As shown in these

Fig. 10 :
Fig.10: Range of variation in speed, torque and power in (%) at t = 1 s.